Setting
Let denote a random vector (corresponding to the measurements), taken from a parametrized family of probability density functions or probability mass functions, which depends on the unknown deterministic parameter . The parameter space is partitioned into two disjoint sets and . Let denote the hypothesis that, and let denote the hypothesis that . The binary test of hypotheses is performed using a test function .
meaning that is in force if the measurement and that is in force if the measurement . Note that is a disjoint covering of the measurement space.
Read more about this topic: Uniformly Most Powerful Test
Famous quotes containing the word setting:
“The new sound-sphere is global. It ripples at great speed across languages, ideologies, frontiers and races.... The economics of this musical esperanto is staggering. Rock and pop breed concentric worlds of fashion, setting and life-style. Popular music has brought with it sociologies of private and public manner, of group solidarity. The politics of Eden come loud.”
—George Steiner (b. 1929)
“Love is at the root of all healthy discipline. The desire to be loved is a powerful motivation for children to behave in ways that give their parents pleasure rather than displeasure. it may even be our own long-ago fear of losing our parents’ love that now sometimes makes us uneasy about setting and maintaining limits. We’re afraid we’ll lose the love of our children when we don’t let them have their way.”
—Fred Rogers (20th century)
“Dandyism is the last flicker of heroism in decadent ages.... Dandyism is a setting sun; like the declining star, it is magnificent, without heat and full of melancholy. But alas! the rising tide of democracy, which spreads everywhere and reduces everything to the same level, is daily carrying away these last champions of human pride, and submerging, in the waters of oblivion, the last traces of these remarkable myrmidons.”
—Charles Baudelaire (1821–1867)